1. Field of the Invention
This invention relates to a method of tightening a screw.
2. Description of the Prior Art
As the method of tightening a screw such as a bolt within a limit of elasticity, there have been known a torque method and an angle method. In the torque method, tightening is terminated when the tightening torque reaches a predetermined value. On the other hand, in the angle method, tightening is terminated when the screw is rotated by a predetermined angle. The torque method is disadvantageous in that it is largely affected by the friction coefficient of the screw and the tightening axial force greatly fluctuates with change of the friction coefficient. For example, when the screw is tightened up to a tightening torque T1 in FIG. 4, the tightening axial force F fluctuates from F1 to F2 as the friction coefficient of the screw .mu. changes from a maximum .mu.max to a minimum .mu.min. Therefore, recently, the angle method has come into wide use. However, also the angle method is affected by the friction coefficient of the screw until the tightening torque reaches the seating torque, and accordingly, an attempt to obtain a high tightening axial force can lead the tightening torque to yielding range Z as shown by range X in FIG. 4.
Further, when the theoretical seating point of the screw is calculated and tightening is terminated when the screw is rotated by a predetermined angle from the theoretical seating point, the affect of the seating torque can be avoided. In this method, though the tightening axial force can be stabilized as compared with the torque method, the maximum tightening axial force must be limited to relatively low value when yield of the screw is taken into account as shown by range Y in FIG. 5.
As can be understood from the description above, it has been difficult to tighten the screw with a maximum axial force close to the limit of elasticity of the screw in accordance with either of the torque method and the angle method.
Generally, the screw yields at a lower tightening axial force as the friction coefficient of the screw increases. This is because not only tensile stress but also torsional stress acts on the screw. The torsional stress .tau. is represented by the following formula. EQU .tau.=16T/nd.sub.1.sup.3 =(8/n)F(d.sub.2 /d.sub.1.sup.3)(1.15.mu.+ tan.beta.) (1)
wherein .tau. represents the torsional stress component, T represents the tightening torque, F represents the tightening axial force, d.sub.1 represents the root diameter of the screw, d.sub.2 represents the effective diameter of the screw, .mu. represents the friction coefficient and .beta. represents the lead angle of the screw.
As can be understood from formula (1), the larger the friction coefficient .mu. is, the larger the torsional stress .tau. and accordingly, the screw yields at a lower tightening axial force as the friction coefficient .mu. of the screw increases. That is, in order to set the maximum tightening axial force close to the limit of elasticity of the screw, optimal tightening must be effected taking into account both the friction coefficient of the screw and the torsional stress.